The 𝐿^{𝑝} norm of sums of translates of a function

Marek, Kanter

doi:10.1090/S0002-9947-1973-0361617-4

The $L^p$ norm of sums of translates of a function
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Trans. Amer. Math. Soc. 179 (1973), 35-47 Request permission

Abstract:

For p not an even integer, $p > 0$, we prove that knowledge of the ${L^p}$ norm of all linear combinations of translates of a real valued function in ${L^p}(R)$ determines the function up to translation and multiplication by $\pm 1$.

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